Global stability of a delayed SIRS epidemic model with saturation incidence and temporary immunity

Computers and Mathematics with Applications

Volumn 59, Issue 9, 2010, Pages 3211-3221

  Xu, Rui ^a   Ma, Zhien ^b   Wang, Zhiping ^a  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Bifurcation; Saturation incidence; SIRS epidemic model; Stability; Temporary immunity; Time delay

Indexed keywords

BASIC REPRODUCTION NUMBER; CHARACTERISTIC EQUATION; DISEASE-FREE EQUILIBRIUM; ENDEMIC EQUILIBRIUM; FIXED PERIOD; GLOBAL ASYMPTOTIC STABILITY; GLOBAL STABILITY; GLOBALLY ASYMPTOTICALLY STABLE; ITERATION TECHNIQUES; LOCAL STABILITY; NUMERICAL SIMULATION; SATURATION INCIDENCE; SIRS EPIDEMIC MODEL; SUFFICIENT CONDITIONS; TEMPORARY IMMUNITY; THEORETICAL RESULT;

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; TIME DELAY;

EPIDEMIOLOGY;

EID: 77950845517     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.03.009     Document Type: Article

References (18)

1. Beretta E., Hara T., Ma W., and Takeuchi Y. Global asymptotic stability of an SIR epidemic model with distributed time delay. Nonlinear Anal. 47 (2001) 4107-4115
2. Beretta E., and Takeuchi Y. Global stability of an SIR epidemic model with time delays. J. Math. Biol. 33 (1995) 250-260
3. Beretta E., and Takeuchi Y. Convergence results in SIR epidemic model with varying population sizes. Nonlinear Anal. 28 (1997) 1909-1921
4. Cooke K.L. Stability analysis for a vector disease model. Rocky Mountain J. Math. 9 (1979) 31-42
5. Gao S., Chen L., Nieto J., and Torres A. Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. Vaccine 24 (2006) 6037-6045
6. Kyrychkoa Y.N., and Blyuss K.B. Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate. Nonlinear Anal. Real World Appl. 6 (2005) 495-507
7. Ma W., Song M., and Takeuchi Y. Global stability of an SIR epidemic model with time delay. Appl. Math. Lett. 17 (2004) 1141-1145
8. Ma W., Takeuchi Y., Hara T., and Beretta E. Permanence of an SIR epidemic model with distributed time delays. Tohoku Math. J. 54 (2002) 581-591
9. Takeuchi Y., and Ma W. Stability analysis on a delayed SIR epidemic model with density dependent birth process. Dyn. Contin. Discrete Impuls. Syst. 5 (1999) 171-184
10. Takeuchi Y., Ma W., and Beretta E. Global asymptotic properties of a SIR epidemic model with finite incubation time. Nonlinear Anal. 42 (2000) 931-947
11. Wen L., and Yang X. Global stability of a delayed SIRS model with temporary immunity. Chaos Solitons Fractals 38 (2008) 221-226
12. Zhang T., and Teng Z. Global behavior and permanence of SIRS epidemic model with time delay. Nonlinear Anal. Real World Appl. 9 (2008) 1409-1424
13. Brauer F., van den Driessche P., and Wang L. Oscillations in a patchy environment disease model. Math. Biosci. 215 (2008) 1-10
14. Capasso V., and Serio G. A generalization of the Kermack-Mckendrick deterministic epidemic model. Math. Biosci. 42 (1978) 41-61
15. Liu W.M., Hethcote H.W., and Levin S.A. Dynamical behavior of epidemiological models with nonlinear incidence rates. J. Math. Biol. 25 (1987) 359-380
16. Liu W.M., Levin S.A., and Iwasa Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J. Math. Biol. 23 (1986) 187-204
17. Hale J. Theory of Functional Differential Equations (1977), Springer-Verlag, Heidelberg
18. Beretta E., and Kuang Y. Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J. Math. Anal. 33 (2002) 1144-1165